9514 1404 393
Answer:
- 67.5 minutes
- G(t) = 188·2^(-t/67.5)
- G(2) ≈ 184.18 g
Step-by-step explanation:
The proportion remaining after 270 minutes is ...
(11.75 g)/(188 g) = 0.0625 = 1/16 = 2^-4
That is, 270 minutes represents 4 half-lives. One half-life is ...
(270 min)/4 = 67.5 min . . . half-life of goo
__
Then the equation for the amount remaining can be written as ...
G(t) = 188×(1/2)^(t/67.5)
G(t) = 188·2^(-t/67.5)
__
After two minutes, the amount remaining is ...
G(2) = 188·2^(-2/67.5) ≈ 184.18 . . . grams
_____
Additional comment
The formula for G(t) can be written numerous ways. My preference is to use numbers from the problem statement so that no rounding is required. If you like, you can express the formula using 'e', the base of natural logarithms.
G(t) = 188·e^(-0.0102688t)
Here, the constant in the exponent has been rounded to 6 significant figures.
